Open-label, two-armed, randomized, trial of highly active anti-retroviral drug therapy (HAART) + CD4-zeta gene-modified CD4+ and CD8+ T cells vs. HAART alone in HIV infected patients with undetectable plasma viral load followed by cessation of HAART in both groups. The HAART only group will subsequently be crossed over to receive gene-modified cells following recurrence of viremia and reinitiation of HAART.